It turns out Ed Sheeran’s number knowledge is not so bad, but subtraction is his weak spot.

Last month, I delivered a talk to members of the New Zealand Educational Institute (NZEI Te Riu Roa) in Christchurch. The talk was oversubscribed, limited by the size of the venue.

I explained why the current primary maths curriculum is failing our children and the cognitive science behind it. I demonstrated how to develop algebraic thinking (another big failure of the Numeracy Project) to support computational thinking (in the context of the new Digital Technologies curriculum).

I also responded to teachers’ feedback on the areas their students find particularly difficult. It wasn’t a great surprise to see that subtraction was a common problem.

Ed’s maths quiz and fondness of mathematical symbols inspired me to write a maths-themed version of his Platinum hit “Shape of You”, the deeper meaning of the lyrics revealed in my talk.

“Maths I Can Do” is for New Zealand teachers and their students to sing in their classrooms, but classrooms in other countries may enjoy it too. It is for non-profit educational purposes only. Please do not use it commercially.

Please share as widely as possible to raise awareness of New Zealand’s big maths problem.

At the end of 2014, a representative sample of 6,321 New Zealand Year 5 students with an average age of 10.0 years were surveyed. Out of 49 countries, New Zealand placed 34th, behind all other participating predominantly English-speaking countries. Radio New Zealand put it a little more bluntly.

To be fair, some of the questions were considered too advanced for a New Zealand Year 5 student. However, when restricted to the questions deemed appropriate against the New Zealand Year 5 National Standards, the average student answered fewer than half of those questions correctly.

And yet, the National Standards data for 2014 tells us that 73.2% of New Zealand Year 5 students were at or above the National Standard. If we match this up with the TIMSS international benchmarks, it suggests that some of these students who were at or above the National Standard would probably have been classified as Low achievers in TIMSS.

A student meeting the Low international benchmark “has some basic mathematical knowledge. They can add and subtract whole numbers, have some understanding of multiplication by one-digit numbers, and can solve simple word problems. They have some knowledge of simple fractions, geometric shapes, and measurement. Students can read and complete simple bar graphs and tables.”

This is well below the standard we should expect for a 10-year-old. Now, spare a thought for the students who were classified as Below Low…

16% of our 10-year-old TIMSS participants were Below Low. These students completed fewer than half of the Low benchmark tasks correctly. This is a significant proportion compared to other countries, e.g. England (4%), the United States (5%), Australia (9%). In the top performing countries, less than 1% of their 10-year-olds are Below Low.

More concerning are the statistically significant increases in the large proportions of Māori (26%) and Pasifika (31%) students who were Below Low. If we are going to address the inequality in this country, providing these students with a maths education leading to greater opportunities would be a very good place to start.

I analysed the performance of our TIMSS 10-year-olds, question by question. They were mostly on the wrong side of average, but the stand-out questions were the basic arithmetic questions:

Our current maths curriculum has made our children so bad at basic arithmetic that they’d be better off guessing. Is this a standard to be proud of?

One might claim that it doesn’t matter – maths is not about the numbers, after all. TIMSS dispels that myth. There was a very strong positive correlation between country performance in Number versus both Geometric Shapes and Measures, and Data Display. There was also a very strong positive correlation between country performance in Knowledge versus both Applying and Reasoning. Suffice to say, number knowledge is a very strong predictor of success in all areas of mathematics.

TIMSS informs us that New Zealand has higher proportions of teachers who participate in maths professional development compared to most other countries. Despite all this professional development, student performance has not improved since 2002, so why should we believe that further money spent on teacher training will make any difference?

There is a much cheaper and effective form of professional development. Roll out my recent presentation to members of the New Zealand Educational Institute (NZEI Te Riu Roa) nationwide, and then see the maths that our kids can do.

The latest Trends in Mathematics and Science Study (TIMSS) data has been released. At first glance, it looks like New Zealand’s maths scores have improved since 2010, but unfortunately we cannot be certain of this. The scores are published with a statistical margin of error, which means that if we were to run the survey again with different samples of children, we might not see the same “improvement”. If we include the published margins of error, we see overlapping bands of achievement rather than increasing lines from 2010 to 2014. In fact, over 20 years, New Zealand’s performance has been disappointly consistent. We’re still below average.

The Ministry of Education has been honest and sober in its reporting, but nevertheless, the Minister of Education has said, in congratulatory tones, that average scores had increased! How can she claim there is an improvement when her own officials say that scores haven’t changed? Is she wilfully ignoring them, or does she needs a lesson on how to interpret statistical reports?

There was some encouraging growth in Year 5 students working at an “advanced” level, but at the other end of the spectrum, less than half of the student samples were working at the desired level of mathematics in the New Zealand Curriculum, and when looking at only the TIMSS questions which fit with New Zealand curriculum expectations, the average student answered just under half of these questions correctly. We have a high proportion of under-achieving students compared to other countries, and at the Year 9 level, this proportion has grown since 1995.

The Bring Back Column Addition Campaign was launched in response to New Zealand’s poor performance in TIMSS 2011(*). It would appear there is no reason to stop campaigning. We asked for some simple, pragmatic changes to the curriculum that would allow under-achieving students to progress. Without them, any improvements are likely to remain statistically insignificant.

Dr Audrey Tan, Mathmo Consulting
29 November 2016

(*) Internationally, TIMSS data is labelled by the odd-numbered years in which students in the northern hemisphere are assessed. New Zealand students are assessed at the end of the year prior, hence the even-numbered years referred to in the Ministry’s reports.

It’s time for New Zealand to look past the hysterical response to this year’s NCEA Level 1 MCAT exam and try to understand what’s really going on here.

Was the exam appropriate in level and difficulty?

In my previous post, I analysed the second of the two (supposedly) parallel papers and found that most of the questions were at a reasonable level for NCEA Level 1, and also reflective of the title “Apply algebraic procedures in solving problems”.

There was a section that was more investigative in nature and new for MCAT (but such questions have appeared in other Level 1 maths assessments in the past). This section was made difficult by its poor construction and confusing wording, and most Level 1 students would have struggled to understand the intention. But most exams have a Very Hard Question (VHQ), so I guess this is the VHQ for this exam.

Was it too different from previous years?

Apart from the investigative question, I don’t think so, but I might have said differently last year, when there was a noticeable step up. From the 2015 MCAT Exemplar:

“This year at least one of the three questions will not have any directed straight procedure-based parts and the other questions a maximum of one such part.…candidates will not be able to provide evidence by following a direction to solve factorised quadratics, factorise, expand, write or solve a linear equation, or simplify an expression involving the collection of like terms in response to being told to. One part in each question may direct the student to perform such procedures; but without further evidence at Achievement level, this will not be sufficient for the award of the standard. Utilising procedures such as factorising, simplifying a rational function, or writing an equation from a word problem will provide evidence of solving a problem. Candidates must know that given a word problem, they will be required to write equation(s) and demonstrate consistent use of these in solving a problem. Candidates will be expected to have a basic understanding of the relationship between a quadratic function and the associated graph.”

MCAT was last reviewed in 2013 and is up for review at the end of this year. Whether a change in style between reviews is appropriate should certainly be up for discussion.

So why did students find it so difficult?

The unfortunate reality is that students did struggle with this exam. The gap between what MCAT is expecting of students, and what students are actually capable of, is widening.

There are complaints that the lack of “gimme” questions at the start of the paper has left students “shell-shocked” and “killed” their confidence. Are we seriously saying that our students are capable of factorising a quadratic when explicitly told to do so, but they are unable to decode a basic word problem and factorise a supplied quadratic expression for themselves, even though they probably wouldn’t know of anything else to do with an expanded quadratic? What does this say about the resourcefulness or resilience of our students?

We cannot blame this year’s Level 1 maths teachers for what has happened, and they should rightly feel insulted. The problem started many years before this one.

What we’re really seeing here is the fruits of a flawed primary maths curriculum floating its way through the system. Even two and a half years at secondary school isn’t enough to turn things around. The damage is too great.

If you look at what the Numeracy Project was trying to achieve at primary school level, our secondary school students should, by all accounts, be highly numerate problem solvers, but in fact they are worryingly innumerate and apparently not very good problem solvers either. It’s ironic that one of the big selling points of this “new approach” to teaching maths was the development of early “Algebraic Thinking”. I think we can safely call that a Not Achieved.

A systemic failure in mathematics education is playing out before our very eyes. NZQA is trying to inch up the standard, year by year, when the reality is that students are actually getting worse at algebra, year by year. When students are struggling to master the basics, it’s hard to see how teachers can lift their students to the higher levels of problem solving now expected.

Given that next year’s Year 11 students will be the same generation of 9-year-olds who performed so abysmally in TIMSS 2011, alarm bells should be ringing loudly. It would not be surprising if fewer students were entered for next year’s MCAT.

Spring forward, fall back

NZQA could make the MCAT easier again, but that would be disappointing. I believe this year’s MCAT is the standard we should be aspiring to. If the examination team could tighten up on the construction of certain questions, the MCAT would be an examination to be proud of on the world stage. (The assessment side of things, however, needs a lot more work.)

The best thing NZQA can do is go back to examining algebra at the end of the year.

September is a really bad time of year for students to face their first high-stakes external examination. Some students barely appreciate its significance when it is tangled up with mock exams for other topics and different subjects, and the ones that do appreciate its significance prioritise the MCAT at the expense of preparing for their mock exams.

The sensible thing to do, surely, is to fold it in with “Tables, Equations and Graphs”. We’re already seeing questions about graphs in the MCAT anyway, and why shouldn’t we? Algebra and Graphs are not separate topics, they are inextricably tied. As we now see, NCEA’s compartmentalising of topics as separate assessments is hurting students’ ability to make connections and become effective problem solvers.

The decision to deliver the assessment earlier in the year and have it administered by the schools has a distinct whiff of cost-cutting about it, but it has been a disaster for maths education and is costing the country dearly. If we want students to pursue STEM subjects at university, we need to give them every chance of succeeding in algebra at Level 1, as this effectively marks the fork in the road between calculus and statistics at Level 2. If we want to increase the “dollar value” of Kiwis contributing to New Zealand’s economy, fixing our maths education system is a very good place to start.

Such patronising recommendations from so-called “specialists” highlight the lack of understanding in New Zealand of what success in maths looks like. It is scandalous that the Ministry of Education continues to cling on to flawed ideals created by people who have no mathematical qualifications or experience, despite every indication our children are failing, year after year. They claim that implementing effective maths teaching and learning in classrooms is “challenging and complex”. It gives the impression they’d rather see students continue to fail at maths than acknowledge the compelling evidence of a quick and effective solution.

The Bring Back Column Addition campaign was never supposed to be a long-term crusade. I thought common sense would prevail; how wrong I was, and how much I have learned about attitudes within the education sector. This campaign will continue until the Minister of Education and her officials acknowledge that the acquisition of basic maths skills is not negotiable. Every child should leave primary school knowing their single digit addition and multiplication facts as well as they know their alphabet. They should be able to add, subtract, multiply and divide numbers fluently. They should be able to work confidently with fractions, decimals and percentages. As clients of the system, every parent should demand this.

Education professor John O’Neill says it would take 20 years to pull this country out of its downward spiral. It may well take that long, but while there are still some practising teachers who can remember life before the dreadful Numeracy Project was dispersed over the country like a gas bomb, let’s harness that experience and give our current children a fighting chance. Teachers, please let your students line up the columns and get them doing maths again. It’s the least you can do for our kids and our country.

I have said very little in public about the New Zealand flag referendum, apart from suggesting that the referendum should have been funded by the sale of tea towels. If everyone who voted correctly in the first referendum bought a tea towel of their preferred flag for approximately $25, that would have covered the estimated $26 million. Given the Prime Minister’s financial acumen, I’m surprised he didn’t think of that himself.

Instead, New Zealand’s coffers are $26 million poorer and our Prime Minister is still chasing a legacy.